Matthiessen's rule

Matthiessen's rule approximates the total electrical resistivity of a metal by the sum of separate scattering contributions. For a common parabolic energy band, approximately independent scattering mechanisms give $1/\tau ={\sum }_{j}1/{\tau }_j$ for the respective momentum relaxation times, and hence ${\rho }_{\mathrm{el}}=m/(n{e}^2\tau )={\sum }_{j}m/(n{e}^2{\tau }_j)$. Correlated scattering, strongly angle-dependent processes or a complicated changing energy band structure can invalidate the simple addition.